Mathematics and Chess in Ancient Egypt
by Dr. Uvencio Blanco Hernández
“In India, as with Egypt, the origin of mathematics is associated with religious rituals. Mathematically, the Indian origin of the decimal numbering system and the rules of calculus is considered indisputable”.
The fractions of the “Eye of Horus”
Most studies affirm that, without a doubt, Ancient Egypt was the greatest technological civilisation of antiquity; the triumph of human practice, efficiency and intelligence. It is estimated to have developed from 3000 BC after the unification of Upper and Lower Egypt and lasted for approximately three millennia.
Its authors explain that due to the growing need to solve everyday problems associated with crops, construction and trade, the Egyptians created their own numbering system; an arithmetic with the four basic operations (addition, subtraction, multiplication and division) and units of measurement of length, area, volume, weight and time.
The Egyptian numbering system also made it possible to represent numbers, from one to millions, from the beginning of the use of hieroglyphic writing; they also had the first developed decimal system – base 10 numeration – which, although not a positional system, allowed the use of large numbers and also to describe small quantities in the form of unit fractions: the so-called Eye of Horus fractions.
Archaeological evidence concerning the knowledge of such methods of calculation comes from inscriptions carved on stones, from calendars and above all from some papyri. Two of the oldest papyri are particularly noteworthy: the Golenischevse papyrus preserved in the city of Moscow and the Rhind or Ahmes papyrus in the British Museum in London.
The Egyptians reached a high level in arithmetical manipulations but their methods were primitive and without great generalisations; there is almost no symbolism in them because the Egyptians were not given to abstract research.
Although the Egyptians worked mainly in geometry and arithmetic, the Egyptians made great contributions to mathematics because they knew how to calculate the surface, the volume of pyramids, cylinder and sphere, algebra, the solar calendar in astronomy, sundials (gnomes) and water clocks (clepsydras). Because of these contributions their growth was important; so much so that the most prominent Greek mathematicians travelled to Egypt and Babylon to learn from these peoples.
Zero and negative numbers in a culture born in Hindustan
For its part, Indian mathematics has made important contributions, as well as a notable influence on Arab mathematics and, through it, on Western mathematics.
The oldest extant records from India are the Sulba Sutras (dating from about the 8th century BC to the 2nd century AD), appendices of religious texts with simple rules for constructing altars of various shapes, such as squares, rectangles, parallelograms and others. As with Egypt, the origin of mathematics is associated with religious rituals.
For example, in the Sulba Sutras there are methods for constructing circles with approximately the same area as a square, which involves many different approximations of the number π. Additionally, they obtained the value of the square root of 2 with various approximation figures, lists of Pythagorean terns and the statement of the Pythagorean theorem.
All these results are present in Babylonian mathematics, which indicates a strong Mesopotamian influence, although very few mathematical documents have come down to us, despite the high cultural level of this civilisation.
Even more than in the case of China, there is a tremendous lack of continuity in the Hindu mathematical tradition and, as was the case with earlier civilisations, there is no theoretical formalism of any kind. The main characteristic of mathematical development in this culture is the predominance of the arithmetical rules of calculation, highlighting the correct use of negative numbers and the introduction of zero, even accepting irrational numbers as valid numbers.
To sum up, we will conclude by saying that in the history of India there are enough facts that show the existence of political and economic relations with the Greek, Egyptian, Arab and Chinese states. Mathematically, the Indian origin of the decimal numbering system and the rules of calculus is considered indisputable.
Blanco, U. (2020). “Ajedrez patrimonio cultural de la humanidad”